Find the volume of the figure shown below.
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Answer:
Step-by-step explanation:
The slope formula is
Filling in this formula with 2 different points 2 times will ensure that this is fact a linear function. In other words, if the slope comes up the same between points 1 and 2 and then between points 2 and 3, this is linear.
Between (0, 600) and (3, 720) the slope formula is
and
So this is in fact linear because the slopes are the same.
Interpreting a slope is similar to interpreting a unit ratio. In our case, the slope means that after the initial investment in the account, $40 per day (there's the unit rate I was referring to) is deposited into the account.
Using that slope to write first the point-slope form of the line allows us to use any one of the 3 coordinates to write the equation. I use (0, 600). In point-slope form:
That's point-slope form. Now for slope-intercept form, which is the same as solving for y.
y - 600 = 40x - 0 and
y = 40x + 600. That's slope-intercept, and now for standard form. Standard form follows the format of a. No fractions and b. Both the x and y terms go on the same side of the equals sign and the constant on the other.
We move the x term over to the y side:
-40x + y = 600. But a lot of textbooks don't like to lead with a negative, so the equivalent form of this with a positive leading coefficient is
40x - y = -600 (notice that all we did was change ALL the signs to the opposite of what they were, not just the sign on the x term. Very important!!)